You can find here slides for tutorials and courses that cover the topics of
A primer on optimal transport, NIPS 2017 Tutorial,
Numerical Optimal Transport, undergraduate course
Optimal Transport for Imaging and Learning
: introduction to OT and its application.
Numerical Optimal Transport and Applications
: similar but with more mathematics.
From Monge-Kantorovich to Gromov-Wasserstein
: introcution to Gromov-Wasserstein.
Le transport optimal et ses applications
: introduction slides, in French.